Quantum Theories, Misc

In this paper I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non- Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement many physicists, Galilei invariance (...) is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally I show how this favors a nomological rather than an ontological view of the wave function. (shrink)

In this paper I present the common structure of quantum theories with a primitive ontology, and discuss in what sense the classical world emerges from quantum theories as understood in this framework. In addition, I argue that the primitive ontology approach is better at answering this question than the rival wave function ontology approach or any other approach in which the classical world is nonreductively ‘emergent:’ even if the classical limit within this framework needs to be fully developed, the difficulties (...) are technical rather than conceptual, while this is not true for the alternatives. (shrink)

The aim of this paper is to summarize a particular approach of doing metaphysics through physics - the primitive ontology approach. The idea is that any fundamental physical theory has a well-defined architecture, to the foundation of which there is the primitive ontology, which represents matter. According to the framework provided by this approach when applied to quantum mechanics, the wave function is not suitable to represent matter. Rather, the wave function has a nomological character, given that its role in (...) the theory is to implement the law of evolution for the primitive ontology. (shrink)

It has been argued that the transition from classical to quantum mechanics is an example of a Kuhnian scientific revolution, in which there is a shift from the simple, intuitive, straightforward classical paradigm, to the quantum, convoluted, counterintuitive, amazing new quantum paradigm. In this paper, after having clarified what these quantum paradigms are supposed to be, I analyze whether they constitute a radical departure from the classical paradigm. Contrary to what is commonly maintained, I argue that, in addition to radical (...) quantum paradigms, there are also legitimate ways of understanding the quantum world that do not require any substantial change to the classical paradigm. (shrink)

Book Review of: Dow We Really Understand Quantum Mechanics? by Franck Laloe.

Quantum theories constructed on the noncommutative spacetime called the Groenewold–Moyal plane exhibit many interesting properties such as Lorentz and CPT noninvariance, causality violation and twisted statistics. We show that such violations lead to many striking features that may be tested experimentally. These theories predict Pauli forbidden transitions due to twisted statistics, anisotropies in the cosmic microwave background radiation due to correlations of observables in spacelike regions and Lorentz and CPT violations in scattering amplitudes.

This note, in rejoinder to a paper by Newton critical of our analysis of certain limitations of quantum scattering theory, seeks to acknowledge and to clarify the disparate interests of the two conflicting articles.

When quantum scattering theory is applied strictly from the point of view that the state of a system is completely described by the density matrix, whether pure or mixed, it is not possible to assume that colliding particles are at all times individually in pure states. Exact results are significantly different from conventionally accepted approximations. In particular, it turns out that the cross section as ordinarily defined in theS-matrix formalism is an adequate parameter for deciding the outcome of interactions only (...) when the particles are carefully prepared in matching pure states. In general the use of the cross section in studying pair collisions in a real gas is shown to be analogous to a repeated “collapse of the wave function” after each collision, and involves arbitrary removal of nondiagonal elements of the density matrix, thus violating the basic laws of quantum dynamical evolution. (shrink)

A generalized Onsager reciprocity theorem emerges as an exact consequence of the structure of the nonlinear equation of motion of quantum thermodynamics and is valid for all the dissipative nonequilibrium states, close and far from stable thermodynamic equilibrium, of an isolated system composed of a single constituent of matter with a finite-dimensional Hilbert space. In addition, a dispersion-dissipation theorem results in a precise relation between the generalized dissipative conductivity that describes the mutual interrelation between dissipative rates of a pair of (...) observables and the codispersions of the same observables and the generators of the motion. These results are presented together with a review of quantum thermodynamic postulates and general results. (shrink)

Standard quantum theory is inadequate to explain the mechanisms by which potential becomes actual. It is inadequate and therefore unable to describe generation of events. Niels Bohr emphasized long ago that the classical part of the world is necessary. John Bell stressed the same point: that “measurement≓ cannot even be defined within the standard quantum theory, and he sought a solution within hidden variable theories and his concept of “beables.≓Today it is customary to try to explain emergence of the classical (...) world through a decoherence mechanism due to “environment.≓ But, we believe, as it was with the concept of measurement, “environment≓ itself cannot be defined within the standard quantum theory.We have proposed a semiphenomenological solution to this problem by introducing explicitly, from the very beginning, classical degrees of freedom, and by coupling these degrees of freedom, through a Lindblad type coupling, to the quantum world. The resulting theory, we call “event-enhanced quantum theory.≓ EEQT allows us to describe an event-generating mechanism for individual quantum systems under continuous observation. The objections of John Bell are met and precise definitions of an “experiment≓ and of a “measurement≓ have been given within EEQT. However EEQT is, essentially, a nonrelativistic theory.In the present paper we extend the ideas of L. P. Horwitz and C. Piron and we propose a relativistic version of EEQT, with an event-generating algorithm for spin one-half particle detectors. The algorithm is based on proper time formulation of the relalivistic quantum theory. Although we use indefinite metric, all the probabilities controlling the random process of the detector clicks are nonnegative. (shrink)

In this paper, we discuss the general significance of order in physics, as a first step toward the development of new notions of order. We begin with a brief historical discussion of the notions of order underlying ancient Greek views, and then go on to show how these changed in key ways with the rise of classical physics. This leads to a broader view of the significance of order, which helps to indicate what is to be meant by a change (...) of our general notions of order in physics. We then go into relativity and quantum theory, showing how these developments actually did bring in further new notions of order, which are however inconsistent and otherwise inadequate in certain ways. Finally, using these inconsistencies and inadequacies as clues or indications for yet a further new concept of order, we make some proposals for novel directions of inquiry (to be discussed in some detail in later papers) which could lead to theories as different from relativity and quantum theory as these are from classical physics. (shrink)

The spectral fluctuations of quantum (or wave) systems with a chaotic classical (or ray) limit are mostly universal and faithful to random-matrix theory. Taking up ideas of Pechukas and Yukawa we show that equilibrium statistical mechanics for the fictitious gas of particles associated with the parametric motion of levels yields spectral fluctuations of the random-matrix type. Previously known clues to that goal are an appropriate equilibrium ensemble and a certain ergodicity of level dynamics. We here complete the reasoning by establishing (...) a power law for the ħ dependence of the mean parametric separation of avoided level crossings. Due to that law universal spectral fluctuations emerge as average behavior of a family of quantum dynamics drawn from a control parameter interval which becomes vanishingly small in the classical limit; the family thus corresponds to a single classical system. We also argue that classically integrable dynamics cannot produce universal spectral fluctuations since their level dynamics resembles a nearly ideal Pechukas–Yukawa gas. (shrink)

With the purpose of introducing a useful tool for researches concerning foundations of quantum mechanics and applications to quantum technologies, here we address three quantumness quantifiers for bipartite optical systems: one is based on sub-shot-noise correlations, one is related to antibunching and one springs from entanglement determination. The specific cases of parametric downconversion seeded by thermal, coherent and squeezed states are discussed in detail.

This work has two objectives. The first is to begin a mathematical formalism appropriate to treating particles which only interact with each otherindirectly due to hypothesized memory effects in a stochastic medium. More specifically we treat a situation in which a sequence of particles consecutively passes through a region (e.g., a measuring apparatus) in such a way that one particle leaves the region before the next one enters. We want to study a situation in which a particle may interact with (...) other particles that previously passed through the system via disturbances made in the region by these previous particles.Second, we apply the type of stochastic process appearing in this context to the stochastic interpretation of quantum mechanics to obtain a modified version of this interpretation. This version is free of many of the criticisms made against the stochastic interpretation of quantum mechanics. (shrink)

The quantum theory of sequential measurements is worked out and is employed to provide an operational analysis of basic measurement theoretical notions such as coexistence, correlations, repeatability, and ideality. The problem of the operational definition of continuous observables is briefly revisited, with a special emphasis on the localization observable. Finally, a brief overview is given of possible applications of the theory to various fields and problems in quantum physics.

Onc of thc problems of quantnun cosmology follows from thc fact that thc Hamiltonian H of classical general relativity equals zero. Quantizing canonically in thc Schrodinger picture, thc Schrodinger equation for thc wave function *1* of thc universe is thcreforc thc so-called Whcelc:r—DeWitt..

We extend to curved space-time the field theory on R×S3 topology in which field equations were obtained for scalar particles, spin one-half particles, the electromagnetic field of magnetic moments, an SU2 gauge theory, and a Schrödinger-type equation, as compared to ordinary field equations that are formulated on a Minkowskian metric. The theory obtained is an angular-momentum representation of gravitation. Gravitational field equations are presented and compared to the Einstein field equations, and the mathematical and physical similarity and differences between them (...) are pointed out. The problem of motion is discussed, and the equations of motion of a rigid body are developed and given explicitly. One result which is worth emphazing is that while general relativity theory yields Newton's law of motion in the lowest approximation, our theory gives Euler's equations of motion for a rigid body in its lowest approximation. (shrink)

The ’microcausality’ condition in quantum field theory is typically presented and justified on the basis of general principles of physical causality. I explore in detail a number of alternative causal interpretations of this condition. I conclude that none is fully satisfactory, independent of further and controversial assumptions about the object and scope of quantum field theories. In particular the stronger causalreadings require a fully reductionist and fundamentalist attitude to quantum field theory. I argue, in a deflationary spirit, for a reading (...) of the ‘microcausality’ condition as merely a boundary condition, inspired by Relativity, that different possible formulations of quantum field theory must obey. (shrink)

We review a recent approach to the foundations of quantum mechanics inspired by quantum information theory. The approach is based on a general framework, which allows one to address a large class of physical theories which share basic information-theoretic features. We first illustrate two very primitive features, expressed by the axioms of causality and purity-preservation, which are satisfied by both classical and quantum theory. We then discuss the axiom of purification, which expresses a strong version of the Conservation of Information (...) and captures the core of a vast number of protocols in quantum information. Purification is a highly non-classical feature and leads directly to the emergence of entanglement at the purely conceptual level, without any reference to the superposition principle. Supplemented by a few additional requirements, satisfied by classical and quantum theory, it provides a complete axiomatic characterization of quantum theory for finite dimensional systems. (shrink)

The relevance of observations in introducing time dependence into quantum cosmology is discussed, some of the important features being illustrated by a simple example. Although the concept of time arises in a natural way even with a constant wave function, there are some conceptual difficulties in understanding how arguments which are familiar in classical cosmology translate to the quantum case.

Von Neumann in 1932 was the first to outline the possible non-existence of dispersion free ensembles in quantum mechanics, and he used this basic evidence to give a preliminary proof on incompatibility between quantum mechanics and local hidden variables theory. In the present paper, we give a detailed theoretical elaboration on the manner in which such a fundamental subject could be explored at perceptive and cognitive levels in humans. We also discuss a general design of the experiment that we have (...) in progress so to give direct indications to other researchers engaged in such field. (shrink)

We indicate a new way in the solution of the problem of the quantum measurement . In past papers we used the well-known formalism of the density matrix using an algebraic approach in a two states quantum spin system S, considering the particular case of three anticommuting elements. We demonstrated that, during the wave collapse, we have a transition from the standard Clifford algebra, structured in its space and metrics, to the new spatial structure of the Clifford dihedral algebra. This (...) structured geometric transition, which occurs during the interaction of the S system with the macroscopic measurement system M, causes the destruction of the interferential factors. In the present paper we construct a detailed model of the (S+M) interaction evidencing the particular role of the Time Ordering in the (S+M) coupling since we have a time asymmetric interaction . We demonstrate that , during the measurement , the physical circumstance that the fermion creation and annihilation operators of the S system must be destroyed during such interaction has a fundamental role . (shrink)

In the early 1960s of the 20th century de Broglie was able to explain the cosmological observable red shift, without ad hoc assumptions. Starting from basic quantum considerations he developed his tired light model for the photon. This model explains in a single and beautiful causal way the cosmological redshift without need of assuming the Big Bang and consequently a beginning for the universe. Evidence coming from Earth sciences seems also to confirm these ideas and furthermore concrete proposal of laboratorial (...) scale experiments that can test the model are reviewed. (shrink)

There has been a long-standing and sometimes passionate debate between physicists over whether a dynamical framework for quantum systems should incorporate not completely positive (NCP) maps in addition to completely positive (CP) maps. Despite the reasonableness of the arguments for complete positivity, we argue that NCP maps should be allowed, with a qualification: these should be understood, not as reflecting ‘not completely positive’ evolution, but as linear extensions, to a system’s entire state space, of CP maps that are only partially (...) defined. Beyond the domain of definition of a partial-CP map, we argue, much may be permitted. (shrink)

It is an experimental fact that \ -decays produce in a cloud chamber at most one track and that this track points in a random direction. This seems to contradict the description of decay in Quantum Mechanics: according to Gamow a spherical wave is produced and moves radially according to Schrödinger’s equation. It is as if the interaction with the supersaturated vapor turned the wave into a particle. The aim of this note is to place this effect in the context (...) of Schrödinger’s Quantum Mechanics. We shall see that the properties of the initial wave function suggest the introduction of a semiclassical formalism in which the \ -wave can be described as a collection of semiclassical wavelets; each of them interacts with an atom and forms an entangled state. The interaction can be regarded as a semiclassical inelastic scattering event. The measurement selects the wave function of one of the ions, with a probability given by Born’s rule. This ion interacts with the atoms nearby leading to the formation of a droplet. One can reasonably assume that also the wavelet entangled with the selected ion has probability one to remain as part of the description of the system. The measurement process is therefore represented by a unitary operator. The wavelet remains sharply localized on a classical path \ It is still a probability wave: it determines the probability that another atom be ionized. This probability is essentially zero unless the atom lies on \ . This gives the visible track. (shrink)

In “Quantum Evolution”, Johnjoe McFadden makes far-reaching claims for the importance of quantum physics in the solution of problems in biological science. In this review, I shall discuss the relevance of unitary wavefunction dynamics to biological systems, analyse the inverse quantum Zeno effect, and argue that McFadden’s use of quantum theory is deeply flawed.

The operator structures for the constants of the motion of the relativistic hydrogen atom are examined. ThoughJ 3 andJ · J are constants of the motion,J is not. Its replacement, $\tilde {\rm K}$ , is shown to emerge rather naturally in transforming the equation to spherical coordinates. The separation of variables is presented in hypercomplex number form. This leads to some interesting suggestions regarding the matter/antimatter operator for the Dirac equation.

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability calculus. The previous attempts (...) all required the brackets to take values in ℤ₂. But the usual QM brackets <ψ|ϕ> give the "overlap" between states ψ and ϕ, so for subsets S,T⊆U, the natural definition is <S|T>=|S∩T| (taking values in the natural numbers). This allows QM/sets to be developed with a full probability calculus that turns out to be a non-commutative extension of classical Laplace-Boole finite probability theory. The pedagogical model is illustrated by giving simple treatments of the indeterminacy principle, the double-slit experiment, Bell's Theorem, and identical particles in QM/Sets. A more technical appendix explains the mathematics behind carrying some vector space structures between QM over ℂ and QM/Sets over ℤ₂. (shrink)

The theoretical description of particle decay by a single particle theory requires the use of a probability density in time that is not present in conventional theories. The problem of single particle decay is consistently described here within the context of a single particle, relativistic dynamical theory. We derive experimentally testable differences between the standard model and Relativistic Dynamics for a two-state system: the neutral K-meson (K 0) system. We show that the estimate of mass difference between the two states (...) is theory dependent. (shrink)

The experimental confirmation of nonlocality has renewed interest in Bohm's quantum potential. The construction of quantum potentials for relativistic systems has encountered difficulties which do not arise in a parametrized formulation of relativistic quantum mechanics known as Relativistic Dynamics. The purpose of this paper is to show how to construct a quantum potential in the relativistic domain by deriving a relativistically invariant quantum potential using Relativistic Dynamics. The formalism is applied to three relativistic scalar particle models: a single particle interacting (...) with a scalar potential; N particles interacting with a scalar potential; and a single particle interacting with an electromagnetic 4-vector potential. (shrink)

Recent work in parametrized relativistic quantum theory (PRQT) has shown that oscillations between mass states are predicted by an alternative formulation of relativistic quantum theory that uses an invariant evolution parameter. A PRQT model of flavor transitions is compared to the standard model. The resulting PRQT expression for the probability of survival of an incident neutrino differs significantly from the standard neutrino oscillation model. Neutrino oscillation measurements provide an experimental testing ground for two theories that are based on fundamentally different (...) concepts of temporal evolution. (shrink)

We wish to determine the correct partial differential equation(s) for describing a relativistic particle. A physical foundation is presented for using a parametrized wave equation with the general form $$i\frac{{\partial \psi }}{{\partial s}} = K\psi$$ where s is the invariant evolution parameter. Several forms have been proposed for the generator K of evolution parameter translations. Of the proposed generators, only the generator K 2 which is proportional to the inner product P μ P μ of fourmomentum operators can be derived (...) from first principles, notably a probabilistic basis. Although experimental tests must be made to establish the validity of K 2,we conclude that K 2 is the leading theoretical candidate for the form of a generator of evolution parameter translations. (shrink)

The problem of a relativistic spin-1/2 particle scattering from a step potential is solved within the theoretical framework of relativistic dynamics. This treatment avoids the Klein paradox. An experiment for testing the theory is suggested.

We show that the divergence between the predictions of quantum optics and the local realist theory known as stochastic optics, for the extended type of photon-coincidence experiment described recently by de Caro, is of the same order of magnitude as for Aspect-type experiments. This means that, in such new experiments, as in those so far performed, counting statistics will have to be greatly improved before a discrimination between the two theories becomes possible.We also show that the outstanding difference between the (...) two theories is that, while stochastic optics uses a genuine, that is, positive, detection probability, the corresponding quantum formalism leads to a pseudoprobability. Nevertheless, there is a striking parallel, in that both theories recognize the phenomenon known as enhancement, and both describe it as having its origin in a mixing of the signal field with the zero-point field by a polarizing device. (shrink)

Using the Q representation, we study the disagreement between quantum optical formalism and local realism and we show that the phenomenon of enhancement, first revealed by the local realist analysis, could receive a simple explanation if we use this particular version of the quantum formalism. Nevertheless, some fundamental difficulties remain.

The possibility of a sub-quantum mechanical realm has been investigated in recent years by DeBroglie, Bohm, Vigier, and others. It is felt that what is needed in this investigation is some simple and direct resolution of the problem as to whether sub-quantum entities exist or not. By restricting attention to quanta of light energy there is presented a theoretical expression for a sub-quantum or micro-photon which has proven to be testable. It is possible by this development to bridge the particle-wave (...) duality wherein these two conceptions become arithmetically commensurate with one another. The theoretical expression derived for the micro-photon also leads to a different interpretative approach to Planck's constant as well as the appearance of a new unit or element of mass. (shrink)

It is shown that the heuristic "derivation" of the Schrödinger equation in quantum mechanics textbooks can be turned into a real derivation by resorting to spacetime translation invariance and relativistic invariance.

The meaning of the wave function and its evolution are investigated. First, we argue that the wave function in quantum mechanics is a description of random discontinuous motion of particles, and the modulus square of the wave function gives the probability density of the particles being in certain locations in space. Next, we show that the linear non-relativistic evolution of the wave function of an isolated system obeys the free Schrödinger equation due to the requirements of spacetime translation invariance and (...) relativistic invariance. Thirdly, we argue that the random discontinuous motion of particles may lead to a stochastic, nonlinear collapse evolution of the wave function. A discrete model of energy-conserved wavefunction collapse is proposed and shown consistent with existing experiments and our macroscopic experience. Besides, we also give a critical analysis of the de Broglie-Bohm theory, the many-worlds interpretation and other dynamical collapse theories, and briefly discuss the issues of unifying quantum mechanics and relativity. (shrink)

We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has effective mass and charge density distributing in space, proportional to the square of the absolute value of its wave function. In a realistic interpretation, the wave function of a quantum system can be taken as a description of either a physical field or the ergodic motion of a particle. The essential difference (...) between a field and the ergodic motion of a particle lies in the property of simultaneity; a field exists throughout space simultaneously, whereas the ergodic motion of a particle exists throughout space in a time-divided way. If the wave function is a physical field, then the mass and charge density will be distributed in space simultaneously for a charged quantum system, and thus there will exist gravitational and electrostatic self-interactions of its wave function. This not only violates the superposition principle of quantum mechanics but also contradicts experimental observations. Thus the wave function cannot be a description of a physical field but a description of the ergodic motion of a particle. For the later there is only a localized particle with mass and charge at every instant, and thus there will not exist any self-interaction for the wave function. Which kind of ergodic motion of particles then? It is argued that the classical ergodic models, which assume continuous motion of particles, cannot be consistent with quantum mechanics. Based on the negative result, we suggest that the wave function is a description of the quantum motion of particles, which is random and discontinuous in nature. On this interpretation, the square of the absolute value of the wave function not only gives the probability of the particle being found in certain locations, but also gives the probability of the particle being there. We show that this new interpretation of the wave function provides a natural realistic alternative to the orthodox interpretation, and its implications for other realistic interpretations of quantum mechanics are also briefly discussed. (shrink)

Feynman's sum-over-histories formulation of quantum mechanics has been considered a useful calculational tool in which virtual Feynman histories entering into a coherent quantum superposition cannot be individually measured. Here we show that sequential weak values, inferred by consecutive weak measurements of projectors, allow direct experimental probing of individual virtual Feynman histories, thereby revealing the exact nature of quantum interference of coherently superposed histories. Because the total sum of sequential weak values of multitime projection operators for a complete set of orthogonal (...) quantum histories is unity, complete sets of weak values could be interpreted in agreement with the standard quantum mechanical picture. We also elucidate the relationship between sequential weak values of quantum histories with different coarse graining in time and establish the incompatibility of weak values for nonorthogonal quantum histories in history Hilbert space. Bridging theory and experiment, the presented results may enhance our understanding of both weak values and quantum histories. (shrink)

We derive for Bohmian mechanics topological factors for quantum systems with a multiply-connected configuration space Q. These include nonabelian factors corresponding to what we call holonomy-twisted representations of the fundamental group of Q. We employ wave functions on the universal covering space of Q. As a byproduct of our analysis, we obtain an explanation, within the framework of Bohmian mechanics, of the fact that the wave function of a system of identical particles is either symmetric or anti-symmetric.

We review two lines of argument regarding the problem of time in quantum cosmology and in quantum gravity, one that invokes the path integral formalism for quantum gravity to state the absence of time between two three-geometries, and another that defends the absence of time, as a fundamental notion in physics, in terms of: (a) the configuration space argument, put forward by Barbour, Smolin and Kauffman, and (b) the Wheeler-DeWitt equation. We argue that although being correct with respect to a (...) space-time dependent physical chronometrizable clock-time frame, both of these lines of argument fail with respect to a general sense of temporality, expressed in terms of the more elementary notions of a before and an after of a quantum computation. With respect to the first line of argument, it is shown that the early works on the subject address two kinds of temporalities, one that is the space-time geometric dependent temporality, which coincides with the usual definition of a space-time dependent physical chronometrizable clock-time frame, the other is a temporality associated to the notions of input and output of a general quantum gravity computation, that is expressed, in the theoretical discourse of quantum gravity, through the usage of the concepts of: (1) propagation of a wave functional in superspace, as addressed by Wheeler; (2) transition amplitudes of three-geometries and (3) the pathintegral formalism, used to calculate such amplitudes, as addressed by Hartle and Hawking. While the first temporality (space-time dependent temporality) disappears from the theory, the second plays a fundamental role, not only in the several aspects of the theory’s construction, but in the clock-time independence as well, as Wheeler showed. Given this notion of time, different from a chronometrizable, space-time geometry internal notion, we search for a general mathematical and logical structure that is capable of addressing it from a formal point of view. This is done through a family of mathematical structures that is more general than the mathematical category. These structures not only will allow us to address the nature of the temporality present in the transition amplitudes between two three-geometries, but they will also allow us to refute the configuration space argument and to show how a static clock-time-independent quantum state, can be put into a non-clock-time processual expression in terms of fine-grained computational histories, obtained from the relations between different observable’s bases. (shrink)

A formulation of relativistic quantum mechanics is presented independent of the theory of Hilbert space and also independent of the hypothesis of spacetime manifold. A hierarchy is established in the nondistributive lattice of physical ensembles, and it is shown that the projections relating different members of the hierarchy form a semigroup. It is shown how to develop a statistical theory based on the definition of a statistical operator. Involutions defined on the matrix representations of the semigroup are interpreted in terms (...) ofCPT conjugations. The theory of particles of spin one-half and systems with higher spin is developed from first principles. Methods are also developed for defining energy, momentum, orbital angular momentum, and weighted spacetime coordinates without reference to a manifold. (shrink)

Physical phenomena emerge from the quantum fields everywhere in space. However, not only the phenomena emerge from the quantum fields, the law of the conservation of energy must have its origin from the same spatial structure. This paper describes the relations between the main law of physics and the mathematical structure of the “aggregated” quantum fields.

Quantum stochastic models are developed within the framework of a measure entity. An entity is a structure that describes the tests and states of a physical system. A measure entity endows each test with a measure and equips certain sets of states as measurable spaces. A stochastic model consists of measurable realvalued function on the set of states, called a generalized action, together with measures on the measurable state spaces. This structure is then employed to compute quantum probabilities of test (...) outcomes. We characterize those measure entities that are isomorphic to a quantum probability space. We also show that stochastic models provide a phase space description of quantum mechanics and a realistic model of spin. (shrink)